What is RakeSearch?

The enormous size of the diagonal Latin squares space makes it unfeasible to enumerate all its objects straightforwardly in reasonable time. So, in order to discover the structure of this space, sophisticated search methods are needed. In RakeSearch project, we implement an application that picks up separate pairs of mutually orthogonal DLSs, which allows to reconstruct full graphs of their orthogonality.

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User profile Profile Ralfy
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Processing of the square # 17 completed
Dear participants, processing of the square # 17 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 8 9 A B 6 7
2 0 1 5 3 4 A B 6 7 8 9
B 7 9 8 A 6 5 1 3 2 4 0
A 6 8 7 9 B 0 5 1 3 2 4
9 B 7 6 8 A 4 0 5 1 3 2
5 3 4 2 0 1 7 8 9 A B 6
4 5 3 1 2 0 B 6 7 8 9 A
3 4 5 0 1 2 9 A B 6 7 8
6 8 A 9 B 7 1 3 2 4 0 5
7 9 B A 6 8 3 2 4 0 5 1
8 A 6 B 7 9 2 4 0 5 1 3

has 1228403532 orthogonal mates which puts it on the 4th place of the rating among another squares with ~1.2 billion mates!

Now "high part" of spectra of ODLS-12 looks like this (square # 17 marked by red):


Thank you for participation and donation of CPU Time!
20 Jul 2022, 17:24:55 UTC · Discuss


Experiment of calculating the spectra of DLS characteristics
Dear participants!

We start a new joint search with Gerasim@Home project: calculation of spectrum of characteristics of diagonal Latin squares. As mathematical objects, DLS have various numerical characteristics. The spectrum of a characteristic is the range of values it can take. You can read about the scientific background of this new search in presentations of Eduard Vatutin: About Spectra of DLS of small orders and about Spectra of DLS of high orders and volunteer computing grid.
2 Jul 2022, 8:26:26 UTC · Discuss


Processing of the square # 16 completed
Dear folks, processing of the square # 16 is fully completed also! With you help we know, that the square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 9 8 B 6 A 3 5 7
2 0 1 9 3 A 7 B 5 4 8 6
8 A 5 B 7 2 9 4 0 6 1 3
A 5 8 7 6 0 3 9 1 B 2 4
6 B 7 5 8 4 1 0 9 A 3 2
9 3 4 2 0 7 A 8 6 1 B 5
4 9 3 1 2 B 8 5 7 0 6 A
B 7 6 8 A 9 2 1 3 5 4 0
5 8 A 6 B 1 4 3 2 7 0 9
7 6 B A 5 3 0 2 4 8 9 1
3 4 9 0 1 6 5 A B 2 7 8

has 575760702 orthogonal mates which puts it on the 13th place of the rating between square with 357535322 orthogonal mates and square with 780235212 mates. And it is interesting!

Thank you for participation and donation of CPU Time!
22 Jun 2022, 11:21:10 UTC · Discuss


Processing of the square # 15 completed
Dear folks, processing of the square # 15 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 5 3 8 6 7 B 9 A
3 4 5 1 2 0 B 9 A 6 7 8
9 B A 6 8 7 4 3 5 1 0 2
7 6 8 9 B A 1 0 2 3 5 4
6 8 7 B A 9 2 1 0 4 3 5
A 9 B 7 6 8 3 5 4 0 2 1
B A 9 8 7 6 5 4 3 2 1 0
8 7 6 A 9 B 0 2 1 5 4 3
2 0 1 5 3 4 7 8 6 A B 9
5 3 4 0 1 2 9 A B 7 8 6
4 5 3 2 0 1 A B 9 8 6 7

has 780235212 orthogonal mates which puts it on the 12th place of the rating. This square is close to square # 14. Another "brick" into the "bridge" between squares with ~ 1 billion orthogonal mates and 300 millions orthogonal mates.

Thank you for participation and donation of CPU Time!
5 Jun 2022, 17:36:03 UTC · Discuss


Processing of the square # 14 completed
Dear folks, processing of the square # 14 is fully completed! The square:

0 1 2 3 4 5 6 7 8 9 A B
1 2 0 4 9 8 B 6 A 3 5 7
5 8 A 6 B 1 4 3 2 7 0 9
8 A 5 B 7 2 9 4 0 6 1 3
A 5 8 7 6 0 3 9 1 B 2 4
9 3 4 2 0 7 A 8 6 1 B 5
6 B 7 5 8 4 1 0 9 A 3 2
4 9 3 1 2 B 8 5 7 0 6 A
B 7 6 8 A 9 2 1 3 5 4 0
2 0 1 9 3 A 7 B 5 4 8 6
7 6 B A 5 3 0 2 4 8 9 1
3 4 9 0 1 6 5 A B 2 7 8

have 800173600 orthogonal mates which puts it on the 11th place of the rating. This square close to square # 11 and square # 10 and together these square create a "bridge" between the squares with ~ 1 billion orthogonal mates and 300 millions orthogonal mates.

Thank you for participation and donation of CPU Time!
10 May 2022, 6:39:18 UTC · Discuss


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